{"id":"W4392637423","doi":"10.1007/978-3-031-42891-3_4","title":"Polák Theorem","year":2024,"lang":"en","type":"book-chapter","venue":"Synthesis lectures on mathematics and statistics","topic":"semigroups and automata theory","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Lattice (music); Mathematics; Combinatorics; Discrete mathematics; Physics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004346991,0.0009286215,0.0008762676,0.001980204,0.002484326,0.003691006,0.001066147,0.001190554,0.06043382],"category_scores_gemma":[0.001437882,0.0005358084,0.0008398892,0.001420048,0.002709399,0.006170697,0.003108633,0.004891515,0.02113143],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001538814,"about_ca_system_score_gemma":0.001044412,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001442555,"about_ca_topic_score_gemma":0.001239336,"domain_scores_codex":[0.9993667,0.00009712453,0.00002839088,0.0002124663,0.0001869311,0.0001084064],"domain_scores_gemma":[0.9996772,0.00009011111,0.0000186366,0.00008446382,0.00009609335,0.00003359107],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0000190958,0.0000111903,0.00003967129,0.00006475601,0.000005627814,0.00002189662,0.00009372886,0.00008120257,0.0002273372,0.9607466,0.02461195,0.01407692],"study_design_scores_gemma":[0.000008613185,0.000006046751,0.000119118,0.00002424284,0.000009436999,0.000100097,0.00005430623,0.0003163443,0.0003886115,0.8555524,0.1434134,0.00000737956],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"methods","genre_scores_codex":[0.002846044,0.002307069,0.0285772,0.002407219,0.001196684,0.00003627081,0.00062635,0.0002999516,0.9617032],"genre_scores_gemma":[0.1877679,0.005951367,0.01880326,0.005260449,0.001548006,0.0003464479,0.001656908,0.001030238,0.7776354],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.06043382,"threshold_uncertainty_score":0.2021713,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01263921902068846,"score_gpt":0.2271310745874744,"score_spread":0.2144918555667859,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}